Into a hat you place four slips of paper. One has a gold star, one has a red X, and the other two are blank.

Each round will proceed as follows: Each person will select a piece of paper from the hat. Whichever player chooses the slip with the red X joins the "team" of the player who chooses the slip with the gold star. Then all four slips are returned to the hat and the process is repeated. The game ends when all four players are on the same team.

1) On average, how many rounds will the game last until all four players are on the same team?

2) Find a general solution for n players (where the hat contains one gold star, one red X, and n-2 blank slips).

Do the Star and X need to be different symbols? If so then I do not understand the problem at all.

If A&B get teamed in round 1, and C&D get teamed in round 2, would A&D getting teamed in round 3 put them all on the same team? In other words is the equivalent to randomly connecting points until we have a connected graph (where pairs can be chosen more than once?)